Influence of fluid saturation on Rayleigh wave propagation

Abstract

Based on the existing three-phase poroelastic theory, an analytical solution for Rayleigh wave propagation along the traction free, permeable surface of an elastic porous medium, saturated by two immiscible, viscous, compressible fluids, is derived. The analytical expression of the dispersion equation of Rayleigh wave is found to be a cubic polynomial. Through solving the dispersion equation, it is concluded that three different types of Rayleigh wave exist in such medium to be denoted as R1, R2 and R3, respectively. The influences of water saturation on these Rayleigh waves are numerically studied with varying frequencies from 1 Hz to 1 MHz. The results show that water content has significant effects on the velocities and attenuation of the three waves. The amplitudes of the three waves decay in both x - and z - directions, which are parallel to and perpendicular to the propagation direction of the waves, respectively. The R1 wave travels fastest, and the R3 and R2 waves have the second greatest and smallest phase velocities, respectively. The R1 wave is least attenuated, followed by the R2 and R3 waves. The attenuation coefficients of the R2 and R3 waves versus water saturation and excitation frequency have the similar variation trend.